Question

Show that the sum of either pair of opposite angle of cyclic quadrilateral is180°

Answer 1

Given : Let ABCD is cyclic quadrilateral.
To prove : ∠A + ∠C = 180°  and ∠B + ∠D = 180°.
Construction : join OB and OD.
Proof : ∠BOD = 2 ∠BAD
     ∠BAD = 1/2∠ BOD
Similarly ∠BCD = 1/2 ∠DOB
∠BAD + ∠BCD = 1/2∠BOD + 1/2 ∠DOB
                   =1/2(∠ BOD + ∠DOB)
                   = (1/2)X360° = 180°
Similarly ∠B + ∠D = 180°

Answer 2

Given : Let ABCD is cyclic quadrilateral.
To prove : ∠A + ∠C = 180°  and ∠B + ∠D = 180°.
Construction : join OB and OD.

Proof : ∠BOD = 2 ∠BAD
     ∠BAD = 1/2∠ BOD
Similarly ∠BCD = 1/2 ∠DOB
∠BAD + ∠BCD = 1/2∠BOD + 1/2 ∠DOB
                   =1/2(∠ BOD + ∠DOB)
                   = (1/2)X360° = 180°
Similarly ∠B + ∠D = 180°
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